


Pi Day with Plato and Phaedo

by Amuly



Category: Historical RPF, Philosophy - Fandom
Genre: M/M
Language: English
Status: Completed
Published: 2010-03-14
Updated: 2010-03-14
Packaged: 2017-11-04 00:14:56
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 917
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/387522
Author URL: https://archiveofourown.org/users/Amuly/pseuds/Amuly
Summary: <blockquote class="userstuff">
              <p>Plato and Phaedo debate the irrationality of pi.</p>
            </blockquote>





	Pi Day with Plato and Phaedo

Phaedo and Plato were strolling leisurely through Plato’s family’s olive groves. It was a spring day, still chilly, but growing warmer. Plato had grabbed for Phaedo’s hand earlier and was now holding it as they walked, stroking it with his thumb languidly. Plato was happy, walking with Phaedo in the warming, almost spring air.

“Did you hear what the Pythagoreans are saying now?” Plato lifted Phaedo’s hand and kissed it as he asked the question.

“What, some sort of new food restriction? Can we no longer eat olives? Or drink wine?” 

Plato laughed and shook his head. “No, no. Something of much greater importance. Now they’re saying that pi is irrational.”

Phaedo was silent as he considered. “Well, what do we know about pi? It is the ratio of the circumference of a circle to its diameter.”

Plato nodded in agreement. 

“And irrationality is that which cannot be expressed by the ratio of two numbers; yes?”

Again, Plato nodded, but interrupted Phaedo before he could continue. He knew where Phaedo’s logic was leading him, so he preempted it. “However, the numbers of measure for diameter and circumference of circles are imperfect things, wouldn’t you say?”

“How do you mean?”

Plato thought carefully before answering. “I mean, there is no ‘perfect circle’ in existence. Nothing perfectly round exists in the world of flux.”

Plato turned to look at Phaedo as he considered. Phaedo’s eyebrows furrowed for a moment in thought, before his expression smoothed. “But, what do you mean by a ‘perfect circle’? Is this some sort of mystical invention existing in your ideal land of Forms?”

Plato nudged Phaedo teasingly with his shoulder. “Don’t mock. You understand the arguments I make. If I draw one hundred circles, and you draw one hundred circles, they will not all look like they are rounded exactly the same. This is easily understandable, yes?”

Phaedo nodded his head in agreement. “I understand your argument that things differ. However, you then make the jump that somewhere, things must be the same. This is a leap in logic that I cannot accept: a subtle appeal to ignorance fallacy, if you will.” 

Plato sighed. He pulled Phaedo to a stop under one of the olive trees and tugged on his hand as he sat down. Phaedo followed him, and Plato nuzzled contentedly into his side. “You are too focused on the elenchus, none on the dialectic. Tell me, dear Phaedo, how you propose building anything on nothing?”

Phaedo wrapped an arm around Plato, pulling him close. Plato’s eyes closed as he listened to Phaedo press his nose to his hair and inhale deeply. “When you show me a fact based on nothing but reason and certainty, no fallacies, then you can begin to build with your dialectic and sing its praises. Until that day, my philosophy is successfully served by pointing out the flaws in yours.”

Plato sighed in Phaedo’s embrace. “But just think on it, dearest Phaedo. Imagine a circle, perfectly round, with no imperfections. In such a case it certainly seems that the ratio of circumference to diameter would not be a ratio at all, but instead a number of infinite digits, of the likes of the square root of two.”

Plato waited as Phaedo considered. His hand had come up and was stroking his hair gently as he pondered. Phaedo was always so deliberate in his answers. If only Plato could achieve the same patience and consideration in his own life. “But, if an irrational number is one that, by definition, cannot be a ratio of two numbers, doesn’t that mean that pi _cannot_ be irrational, if it is the ratio of circumference to diameter?”

Plato shook his head. “That is assuming the circumference and diameter are rational numbers themselves. Circumference and diameter are just phrases, concepts. They themselves may not conform to such specific rules as rationality.”

Phaedo’s fingers stilled in their movement through Plato’s hair. Concerned that he had said something offensive, Plato looked up at Phaedo. Rather than the disappointment or disagreement Plato was expecting, he saw a small smile gracing Phaedo’s features. Unable to help himself, Plato leaned up and kissed Phaedo on those smiling lips. For a moment Phaedo returned the kiss, before he broke away. “Give me one thousand circles, and we can see if the ratio approaches irrationality as you claim.”

Plato laughed. “Resorting to empiricism are you?”

“Well, when confronted with an un-falsifiable theory…”

Plato pulled back, affecting an appalled expression. “What do you mean, un-falsifiable?”

“Well, you say that either pi is irrational, or that the numbers themselves are irrational, and cause pi to be irrational. Examine the problem from either angle, and your solution holds true.”

“Maybe that just means I’m right.”

“Maybe that just means you’ve invented an implausible and un-falsifiable scenario, resorting to the underhanded tactic of covering all possibilities.”

Abruptly Plato stood and tugged at Phaedo’s arm. “Why don’t we head back to the house and measure circles?”

Phaedo rolled his eyes, but allowed Plato to pull him up to his feet. “I wonder what sort of circle you will have me measure?”

Plato’s eye roll was cut off by a kiss from Phaedo. “I must work on my predictability.”

With a hand on his wrist, Phaedo began pulling him back toward the house. “You don’t need to be any more spontaneous, Plato.”

With that, the two men walked back to Plato’s manor. Plato was eager for Phaedo to measure the circumference of whatever circles he gave him. 

   



End file.
